Table 2 Formulas for the calculation of Hill diversity numbers

N0

Counts the total number of different opinions

P_i

\( {P}_i=\frac{n_i}{N}\kern0.75em i=1,2,3\dots, C \)

Where:

P = proportional abundance of the i-belief:

n_i= frequency of the i-belief

N= total number of T beliefs

P_i is used to obtain diversity indices

Simpson’s diversity index (λ)

\( \uplambda =\sum \limits_{i=1}^s{P}_i^2 \)

Indicates the dominance of some ideas over others, this enabling the degree of agreement about a represented object in a community to be ascertained

Shannon-Weaver diversity index (H’)

\( {H}^{\prime }=-\sum \limits_{i=1}^{S^{\ast }}\left({P}_{i\kern0.5em }\ln {P}_i\right) \)

Where S is the known beliefs with proportions. Indicates the degree of complexity of the representation, wherein, as the number of opinions increases, the value of H’_max tends to be higher

H′_max

H′_max = ln N0

Maximum diversity of opinions

N1

\( \mathrm{N}1={e}^{H^{\prime }} \)

e = 2.71828

Indicates the number of abundant beliefs in the SR.

e is the base of natural logarithms and H’ is Shannon’s diversity index

N2

N2 = 1/λ

Indicates the number of very abundant beliefs in the SR

Information index (I)

I = H′_max − H′

Indicates the amount of information in the SR

Organization index (Q)

\( Q=1-\left(\frac{H^{\prime }}{H_{\mathrm{max}}^{\prime }}\right) \)

Indicates the degree to which the information is organized